Mesoscale system feedback-induced dissipation and noise suppression

ABSTRACT

A high-gain and low-noise negative feedback control (“feedback control”) system can detect charge transfer in quantum systems at room temperatures. The feedback control system can attenuate dissipative coupling between a quantum system and its thermodynamic environment. The feedback control system can be integrated with standard commercial voltage-impedance measurement system, for example, a potentiostat. In one aspect, the feedback control system includes a plurality of electrodes that are configured to electrically couple to a sample, and a feedback mechanism coupled to a first electrode of the plurality of electrodes. The feedback mechanism is configured to detect a potential associated with the sample via the first electrode. The feedback mechanism provides a feedback signal to the sample via a second electrode of the plurality of electrodes, the feedback signal is configured to provide excitation control of the sample at a third electrode of the plurality of electrode.

RELATED APPLICATION

This application is the 35 U.S.C. § 371 national stage entry ofPCT/US2017/029854, filed Apr. 27, 2017, and claims the benefit ofpriority under 35 U.S.C. § 119(e) to U.S. Provisional Patent ApplicationNo. 62/328,798, filed Apr. 28, 2016, titled “MESOSCALE SYSTEMFEEDBACK-INDUCED DISSIPATION AND NOISE SUPPRESSION,” the entiredisclosure of both of which applications are hereby expresslyincorporated herein by reference.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with government support under contractN66001-11-1-4111 awarded by the Defense Advanced Research ProjectsAgency. The government has certain rights to the invention.

TECHNICAL FIELD

The subject matter described herein relates to detection of analytes.

BACKGROUND

A potentiostat is commonly used in electrochemical experiments to probeproperties of a physical system, for example, an electrochemicalinterface between a solid and liquid phase. A potentiostat employs athree electrode system comprising a reference electrode, a workingelectrode and a counter electrode. The potentiostat can operate bymaintaining a fixed potential difference between a working electrode anda reference electrode and measuring the current that flows through theelectrolyte and across the electrode-electrolyte interface via thecounter electrode. For example, in bulk electrolysis experiments, apotentiostat can be used to measure the total charge that hastransferred across an electrochemical interface at a fixed potentialdifference. The measured charge can be indicative of thereduction/oxidation reaction at the interface.

The physical system (e.g., electrode-electrolyte interface) probed bythe potentiostat can include systems that exhibit quantum properties,e.g., transport properties associated with mesoscale phenomena. However,coupling of the quantum systems with their environment (e.g.,surrounding thermodynamic bath) at room temperatures can lead to onsetof classical behavior in quantum systems. Traditional potentiostats arelimited in their ability to detect quantum properties at roomtemperature in electrochemical systems due to, for example, introductionof external noise (e.g., voltage noise) into the quantum system due tocoupling with the electronic system, dissipation forces acting on thequantum system, etc. As a result, quantum phenomena and mesoscalephenomena (phenomena that lie in between the classical andquantum-mechanical regimes of behavior) cannot be detected bytraditional potentiostats. Detection of mesoscale properties can beimportant for novel sensing, timing and communication paradigms.Therefore, it is desirable to develop a potentiostat that can detect andquantify mesoscale phenomena.

SUMMARY

This application provides for a high-gain and low-noise negativefeedback control system that allows for detection of quantum mechanicalsignatures of analytes at room temperature. This can be done bydissipation reduction and noise suppression in charge transfer processin a mesoscale system that includes the analytes.

Accordingly, in one aspect, the invention provides for systems thatinclude at least:

(a) a plurality of electrodes configured to electrically couple to asample; and

(b) a feedback mechanism coupled to a first electrode of the pluralityof electrodes and configured to detect a potential associated with thesample via the first electrode, wherein the feedback mechanism providesa feedback signal to the sample via a second electrode of the pluralityof electrodes, the feedback signal configured to provide excitationcontrol of the sample at a third electrode of the plurality ofelectrodes. In another aspect, the sample is a molecular-scale chargetransfer system. In another aspect, the feedback signal providesexcitation control of the molecular-scale charge transfer system duringelectronic excitation transfer (EET) in the molecular-scale chargetransfer system. In any of the aspects above and herein, the excitationcontrol attenuates dissipation in the molecular-scale charge transfersystem from a surrounding thermodynamic bath. In any of the aspectsabove and herein, the excitation control can reduces dissipativecoupling of one or more vibronic energy levels in the molecular-scalecharge transfer system to an external bath. In any of the aspects aboveand herein, the first, second and third electrodes are a referenceelectrode, a counter electrode and a working electrode of apotentiostat, respectively. In any of the aspects above and herein thefeedback mechanism can include a first negative-feedback amplifierconfigured to generate a first signal based on a difference between thedetected potential and a set potential value. In any of the aspectsabove and herein, the feedback mechanism can include a second negativefeedback amplifier configured to receive the first signal and generatethe feedback signal. In any of the aspects above and herein, the systemcan include a current detection system configured to detect a currentassociated with the second electrode. In any of the aspects above andherein, the detected current is indicative of an analyte in themolecular-scale charge transfer system.

In one aspect, the invention provides for methods of analyte detectionthat include at least: (a) detecting, by a feedback mechanism via afirst electrode of a plurality of electrodes, a potential associatedwith a sample. The plurality of electrodes can be electrically coupledto the sample; (b) generating, by the feedback mechanism, a feedbacksignal; and (c) providing the feedback signal to the sample via a secondelectrode of the plurality of electrodes. The feedback signal can beconfigured to provide excitation control of the sample at a thirdelectrode of the plurality of electrode. In another aspect, the sampleis a molecular-scale charge transfer system. In another aspect, thefeedback signal provides excitation control of the molecular-scalecharge transfer system during electronic excitation transfer (EET) inthe molecular-scale charge transfer system. In any of the aspects aboveand herein, the excitation control attenuates dissipation in themolecular-scale charge transfer system from a surrounding thermodynamicbath. In any of the aspects above and herein, the excitation controlattenuates dissipation in the molecular-scale charge transfer systemfrom a surrounding thermodynamic bath. In any of the aspects above andherein, the excitation control can reduces dissipative coupling of oneor more vibronic energy levels in the molecular-scale charge transfersystem to an external bath. In any of the aspects above and herein, thefirst, second and third electrodes are a reference electrode, a counterelectrode and a working electrode of a potentiostat, respectively. Inany of the aspects above and herein the feedback mechanism can include afirst negative-feedback amplifier configured to generate a first signalbased on a difference between the detected potential and a set potentialvalue. In any of the aspects above and herein, the feedback mechanismcan include a second negative feedback amplifier configured to receivethe first signal and generate the feedback signal. In any of the aspectsabove and herein, the system can include a current detection systemconfigured to detect a current associated with the second electrode. Inany of the aspects above and herein, the detected current is indicativeof an analyte in the molecular-scale charge transfer system.

DESCRIPTION OF DRAWINGS

FIG. 1 illustrates an implementation of a feedback system for a process;

FIG. 2 illustrates an implementation of a potentiostat with a high-gainand low-noise feedback control system;

FIG. 3 illustrates the effect of high-gain and low-noise feedbackcircuit on the power spectral density (PSD) of voltage noise;

FIG. 4A illustrates a circuit model of an oscillator in contact with athermodynamic bath;

FIG. 4B illustrates a three terminal feedback system for the applicationof the signal to the oscillatory system shown in FIG. 4A;

FIG. 5 illustrates a simulation graph for the oscillation amplitudemeasured at C1 in FIG. 4B in response to a small signal AC excitationwith and without feedback;

FIG. 6A illustrates a simulation of voltage noise spectral density forthe oscillator node V_(x) in FIG. 4A without feedback as a function ofX_(r);

FIG. 6B illustrates a simulation of voltage noise spectral density forthe oscillator node V_(x′) in FIG. 4B with feedback as a function ofX_(r);

FIG. 6C illustrates a simulation of voltage noise spectral density forthe oscillator node V_(x′) in FIG. 4B with feedback as a function ofX_(m);

FIG. 7A illustrates a circuit model for a two-state electronicexcitation transfer (EET) system coupled to an external bath ofreservoir modes according to various example embodiments describedherein; and

FIG. 7B illustrates a feedback system coupled to the EET system shown inFIG. 7A for the attenuation of environment-induced dissipation.

DETAILED DESCRIPTION

A high-gain and low-noise negative feedback control (hereinafter“feedback control”) system can detect quantum mechanical signatures incharge transfer occurring within quantum systems at room temperatures.The feedback control system can attenuate dissipative coupling between aquantum system (e.g., vibrionic energy levels) and its thermodynamicenvironment by suppressing intrinsic energy fluctuations (e.g.,fluctuation in electric fields) associated with the quantum system. Thedissipative coupling, which can be prominent at room temperatures, canhinder the detection of quantum phenomena (e.g., transport propertiesassociated with mesoscale phenomena). Measurement architectures with lownoise feedback control system can detect quantum phenomenon at roomtemperature that may not be observed using traditional measurementdevices and techniques.

The feedback control system can be integrated with standard commercialvoltage-impedance measurement system, for example, a potentiostat. Astandard potentiostat has a three electrode circuit topology, and canmeasure electrical properties of an electrochemical system. Theelectrochemical system can include an electrode (e.g., metallic orsemi-conducting), an electrolyte (e.g., an aqueous solvent, an organicsolvent, etc.), a buffering salt, components of a testing sample (e.g.,a complex matrix), one or more analyte species, redox species that canserve as charge source or sink to facilitate charge exchange with theelectrode, etc. The redox species can include, for example,ferro-/ferricyanide couple, ferrocenium ion and ruthenium hexaaminecomplex. The analytes can include, for example, whole microorganisms orcomponents thereof including DNA, RNA oligomers, peptide fragments,proteins, glycans, polysaccharides, metabolites etc. The three electrodecircuit topology includes a counter electrode, a working electrode, anda reference electrode which can be electrically coupled to theelectrochemical system.

The feedback control system can be integrated with a potentiostat, andcan control the potential and/or current at one or more of the threeelectrodes. The feedback control system can be configured to control thepotential of the electrochemical system (e.g., by setting it to adesired value) and/or suppress the voltage noise in the electrochemicalsystem. It can detect the potential of the electrochemical system (e.g.,at the reference electrode) and send a corrective feedback signal (e.g.,current signal, voltage signal) to alter the potential and/or reducevoltage noise associated with the electrochemical system. The correctivefeedback signal can also alter the electronic exchange process at theworking electrode. The feedback control system can include one or morehigh gain amplifiers, which in some implementations, can be cascadedtogether. The feedback system can also include a voltage buffer thatallows for the detection of the potential with minimal effect to theelectrochemical system. For example, the impedance of the voltage bufferfrom the point of view of the electrochemical system can be very high.This can prevent current from the electrochemical system from flowinginto the voltage buffer. As a result, potential of the electrochemicalsystem can be detected with minimal perturbation on the electrochemicalsystem.

Suppression of voltage noise of the electrochemical system can result insuppression of energy fluctuations of the quantum electrochemical system(e.g., in the vicinity of an interface between the electrolyte and aworking electrode). This can result in efficient resonant chargetransfer between, for example, the electrolyte-dissolved redox speciesand the working electrode (e.g., charge transfer between discreteelectronic energy levels of vibration-dressed electronic states in theredox species of the molecular charge transfer system, and energy levelsin the working electrode). The feedback control system can limit themultiple scattering contributions from the thermodynamic bath modeswhich can result in resonant charge transfer.

Due to the suppression of voltage noise and the resulting fluctuationsin the electric field at the electrode-electrolyte interface (e.g.,interface between the electrochemical system and the working electrode),the effect of analytes on the charge transfer process between the redoxspecies and the working electrode can be detected. For example, thecharge transfer process can be modified by the vibrational structure ofthe analytes, which can be discerned from the perturbative effect ofintroducing the analyte on the electrode-electrolyte interface. Bycomparing the analyte-modified charge transfer process with a databasecontaining information related to the effects of various analytes oncharge transfer processes, the analyte can be detected

Detection of analytes based on interaction of the analytes with a chargetransfer process using a low noise potentiostatic feedback controlsystem offers several advantages. For example, some implementationsallow for label- and probe-free chemical/biological detection usinginformation about the vibrational structure of the analyte targets.Further, analyte detection with vibrational mode information does notrequire ultra-low temperatures (sub 20K) and high vacuum (e.g., lessthan 10⁻⁵ Torr) environments. Analytes can be detected at ambientconditions. In some implementation, detection can happen over a largedynamic range (e.g., 1 pg/ml-1 ug/ml), with high sensitivity (e.g., lessthan 1 pg/ml lower limit of detection) and high specificity (e.g., closeto 100%). This concept may be extended to other types of systems, forexample, interface between combinations of solid state metal,semiconductor and insulator junctions.

In one aspect or one embodiment, FIG. 1 illustrates a standard feedbacksystem 100 where the output for a process 102 is used to determine theinput to the process in order to maintain a desired operation of theprocess 102. In FIG. 1, an output 116 of the process 102 is used todetermine a feedback signal 118 by the feedback system 104. The feedbacksignal 118 can be used, along with the input signal 112 to determine theprocess input 114 for the process 102. Determination of the processinput 114 can involve, for example, calculating the difference betweenthe input signal 112 and the feedback signal 118, and amplifying thedifference by a gain stage 108.

FIG. 2 illustrates an implementation of a potentiostatic apparatus 200with a feedback control system coupled to an electrochemical system. Theelectrochemical system 250 can include molecular-scale charge transfersystem (e.g., electrolyte 212 and electrode 204), and analytes containedin the electrolyte phase of the system (not shown). The potentiostaticapparatus 200 and the electrochemical system 250 can be electricallycoupled via one or more of counter electrode 202, working electrode 204and reference electrode 206. The potentiostatic apparatus 200 can applya potential bias across the electrochemical system 250 (e.g., betweenreference electrode 206 and working electrode 204). The applied bias canresult in charge transfer between the redox-active species inelectrolyte 212 and the nanoscale working electrode 204. The exchange ofelectrons between the electrodes and the redox species can lead to anexchange of energy, and is referred to as electron energy transfer(EET). The transport of redox species in the electrochemical system 250can complement the flow of electrons in the potentiostatic apparatus 200and completes the charge flow circuit.

The current flowing into (or out) of the counter electrode 202 can berelated to the exchange of electrons between the redox species and theworking electrode 204, for example when the counter electrode is muchlarger in area than the working electrode and the current flow into thereference electrode 206 is small (e.g., zero). Therefore, measuring thecurrent flowing into (or out) of the counter electrode can be indicativeof the rate and nature of electron exchange at the working electrode 204(or counter electrode 202). The current can be detected, for example, bymeasuring a voltage difference across an impedance (e.g., X_(m))electrically coupled to the counter electrode 202. The voltagedifference can be measured, for example, by using a low noise voltmeteror transimpedance amplifier chain. In some implementations, the rate ofelectron exchange at the working electrode 204 can be detected bymeasuring the current at the working electrode 204 (e.g., by measuring avoltage difference across impedance electrically coupled to the workingelectrode 204).

Electrons in the redox species can occupy vibration-dressed electronicenergy states (also referred to as vibronic states). The electronicexchange between the vibronic states of redox species and the energystates in electrodes can be affected by the environment or thermodynamicbath (e.g., dielectric environment of the solvent). The electronicexchange process can also be affected by the presence of analytes (e.g.,analytes present on or near the surface of the working electrodes) andthe background matrix of the sample being tested. The interactionbetween the polarization modes of the analytes (e.g. slow movingvibrational modes of the analyte species) and the vibronic states ofredox species can perturb the electronic exchange process, or andavailable electronic modes of the analytes can even directly participatein the electron exchange process between the redox species and theworking electrode. The effect of the analyte on the electronic exchangeprocess can be detected by measuring the charge exchange current at theworking electrode (204) electrolyte (212) interface which can bemeasured at the counter electrode 202 (or working electrode 204) asdescribed above. By measuring the current for various input voltagesV_(set), a current versus voltage (I-V) trace for the electrochemicalinterface 250 (which can include the effect of analyte) can begenerated. Analytes in the electrochemical system 250 can befingerprinted (e.g., their I-V trace determined) by quantifying theperturbation introduced by these analytes on the measured chargetransfer flux at the interface.

Thermal disturbances in the electric field energy in proximity to theworking electrode 204 can affect the electronic exchange process at theworking electrode 204. Thermal disturbances can affect the electronicexchange process between the redox species and the electrodes, andtherefore impede the determination of the analyte in the electrochemicalsystem. For example, fluctuations in electric fields can be related, forexample, proportionally to the dissipation forces acting on theelectronic exchange process, which can obfuscate any resonantinteractions present in the electrochemical system. The thermaldisturbance in the electric field can arise due to the intrinsicelectrostatic environment at the electrochemical interface or due toelectronic noise injected from the biasing and current-measurementcircuitry (e.g., from the reference electrode 206, counter electrode 202etc.) coupled to the electrochemical system. Thermal disturbances canscale with the temperature of the system making the detection ofanalytes difficult at ambient conditions (for example, above 50 K).

A feedback control system in the potentiostatic apparatus 200 canmitigate the effect of thermal disturbances and dissipation, andtherefore allow for the detection of analytes, for example, via resonantsignatures in the electronic exchange process at room temperatures. Thefeedback control system can apply the desired bias across theelectrochemical interface between the electrolyte 212 and the workingelectrode 204 utilizing negative feedback, and can suppress intrinsicand extrinsic sources of thermal disturbance.

As shown in FIG. 2, the feedback control system comprises a pair ofultra-low noise amplifiers 210 and 220 that are electrically coupled tothe electrochemical system 250 via the counter electrode 202 and thereference electrode 206. The feedback control system detects thepotential V_(ref_) of the redox active species in the electrolyte 212 atthe reference electrode 206. V_(ref) can be representative of thevibronic energy of the redox species in the charge transfer system 212.

In some implementations, the feedback control system can include a lownoise voltage buffer 260 that can detect the potential V_(ref) withminimal perturbation to the charge transfer system 212. This can beachieved, for example, by designing the voltage buffer 260 to have highimpedance from the perspective of the charge transfer system 212. Asshown in FIG. 2, the voltage buffer comprises cascaded field effecttransistors 262 and 264 (e.g., pMOS, nMOS transisors). Transistor 262(e.g., nMOS transistor) can be electrically connected to a voltagesource with potential +V_(B) at its drain, and to the referenceelectrode 206 (via the reference electrode impedance X_(ref)) at itsgate. The drain of the transistor 264 (e.g., nMOS transistor) can beelectrically connected to the source of the transistor 262 via animpedance R_(B1). The source of the transistor 264 can be electricallyconnected to a voltage source with potential −V_(B) via an impedanceR_(B2). Additionally, the gate of the transistor 264 can also beelectrically connected to the voltage source with potential −V_(B). Thevoltage buffer 260 can generate a voltage signal V_(meas) (at the drainof the transistor 264) which represents the voltage V_(ref) detected bythe voltage buffer 260 at the reference electrode 206.

Pair of cascaded amplifiers 210 and 220 are configured to deliver a highgain, low noise corrective signal to the electrochemical system 250 viathe counter electrode 202. The corrective signal is proportional to thedifference between the potential V_(set) (related to the desiredpotential of the electrochemical system 250) and the detected potentialV_(meas). Amplifier 210 has a gain of A1 and has two inputs: V_(set) (atthe inverting input) and V_(meas) (at the non-inverting input). Theoutput of the amplifier 210 is connected to the inverting input by aresistor R_(F1). The output of the amplifier 210 can also be connectedto an inverting input of a second amplifier 220 via resistor R_(S2). Thenon-inverting input of the amplifier 220 can be connected to a groundpotential. The output of the amplifier 220 can be connected to theinverting input of the amplifier 220 by a resistor R_(F2). Thisarrangement of connecting the output of an amplifier (e.g., 210 and 220)to its inverting input is referred to as negative feedback. Cascadednegative feedback amplifiers (e.g., cascaded amplifiers 210 and 220) canprovide high-gain to an input signal (e.g., difference between V_(set)and V_(meas)) and improve the signal to noise ratio of the outputsignal. For example, the output of the amplifier 210 can be proportionalto the difference between the set voltage V_(set) and the measuredvoltage V_(meas). The output of amplifier 220 can be proportional to thedifference between the input at the inverting input (e.g., output of theamplifier 210) and the input at the non-inverting input (e.g., theground potential value).

The cascaded amplifiers can control the potential of and/or currentflowing into (or out) of the counter electrode 202. The output of theamplifier 220 (corrective feedback signal) can be electrically connectedto the counter electrode 202 via impedance X_(M). The correctivefeedback signal can, for example, set the potential of the counterelectrode 202 to a desired potential (e.g., proportional to V_(set)),inject a corrective current into the electrochemical system 250, etc. Acorrective current signal flowing into (or out) of the counter electrodecan be detected by measuring a potential V_(TIA) across the impedanceX_(M) (e.g., by a voltmeter) and dividing the measured potential V_(TIA)by the impedance X_(M). As described before, by measuring the correctivecurrent flowing into (or out) of the counter electrode for various inputvoltages V_(set), a current versus voltage (I-V) graph can be generated.This I-V trace can contain the “fingerprint” of the analytes in theelectrochemical system, and the identity of the analyte can be detectedby comparing the detected I-V data with I-V data of other analytes.

An analyte (or multiple analytes) in an electrolyte can be detected byelectrically coupling the electrochemical system (analyte and theelectrolyte) to the potentiostatic apparatus 200 via the counterelectrode 202, reference electrode 206 and working electrode 204. A usercan set the voltage at the inverting input of the first amplifier 210(e.g., by using a low noise tunable voltage source). The voltage buffer260 can detect the voltage at the reference electrode without addingextrinsic noise and send a signal with a voltage value (related to thedetected voltage) to the non-inverting input 210 of the first amplifier.Based on the two inputs the cascaded high-gain, low-noise negativefeedback amplifiers (e.g., 210 and 220) send a corrective feedbacksignal (e.g., current signal) to the electrochemical system via thecounter electrode. A feedback detection system in the potentiostaticapparatus 200 (e.g., a voltmeter, an ammeter, etc.) can detect thefeedback signal. The feedback detection system can communicate with acontrol system (e.g., a computing device) that can record informationrelated to the detected feedback. The control system can also controlthe value of the set voltage V_(set). For example, the control systemcan sweep through series of values of the set voltage V_(set), andrecord the corresponding feedback signal. The control system cangenerate a dataset of multiple set voltage values and the correspondingfeedback signal (e.g., current). The control system can compare thegenerated dataset with datasets of feedback responses for otherelectrochemical systems (with different electrolytes, analytes, etc.),and determine the identity of the analyte in the electrochemical systemat hand.

FIG. 3 illustrates the effect of high-gain and low-noise negativefeedback circuit on the power spectral density (PSD) of voltage noise atthe reference node of a potentiostatic apparatus 200. The PSD isindicative of the voltage noise at various frequencies. Plots 302 and304 represent the PSD of voltage noise detected at a reference electrodeof a potentiostat without and with the low noise feedback control,respectively. The potentiostat with low noise feedback (e.g.,potentiostatic apparatus 200) has reduced PSD at the reference electrodeby several orders of magnitude. The reduced fluctuations result in fewerthermal disturbances to the vibronic states of the redox active speciesin the electrolyte from the fluctuating electric field. In addition, thehigh gain of the low-noise feedback control system of the potentiostaticapparatus 200 can attenuate any dissipation from the thermodynamic bathacting on the electron transfer process at the electrochemicalinterface, in contrast to an off-the-shelf potentiostat.

Coupling between the energy levels involved in the electron transferprocess (e.g., vibronic states of redox species, energy levels of themetal electrodes, etc.) with the thermodynamic environment and betweenthemselves can be modeled by circuit elements (e.g., inductors,capacitors, resistors, etc.) described in FIGS. 4A, 4B, 7A and 7B. Forexample, a resistor (e.g., X_(r) in FIGS. 4A and 4B, R₁ and R₂ in FIGS.7A and 7B) represents dissipative coupling to the external environmentand/or adds noise related to thermal fluctuations (e.g., voltage noise)to the energy levels, which are themselves represented by the reactances(capacitances and inductances). The circuit elements (e.g., resistors,inductors and capacitors) dictate the electrostatic relaxation of theelectrochemical interface in response to a time-varying voltage bias,which is usually separable from the much faster dynamics of the nuclearand electronic modes of the system. It can be demonstrated that for ahigh-gain and low-noise negative feedback control system, thedissipative coupling of the participant energy states (e.g., vibronicmodes of redox species) with the environment can attenuated when thetime scale of the feedback response is comparable to the relaxationtime-scale of the electrochemical interface. For example, asdemonstrated in Equations 7.1a and 7.1b, for high-gain (e.g., high valueof the product of A₁A₂) the terms in the denominator of Equations 7.1aand 7.1b that have the damping kernel γ₁₁ tend to zero. This suggeststhat for high-gain, damping in the electron transfer process isattenuated.

The preservation of the superposition of quantum probability amplitudesrequires reduced interactions between the system and bath, or areduction in the number of bath modes that can interact with the system,for the case when the quantum system is coupled to a large number ofmodes. A scheme for preserving interferences between states would enablenew room temperature systems exhibiting quantum behavior that could beapplied to sensing, computing, and energy conversion. As an example,persistent quantum coherent interferences of exciton waves are thoughtto boost the efficiency of EET processes, and by extension, theefficiency of an EET transport-mediated photosynthetic process.

In the context outlined above, the embodiments described herein aredirected to excitation control of mesoscale charge transfer system witha classical electronic negative feedback loop. The embodiments canprolong the resonant interactions between the electronic and vibrationalmodes in the electrochemical system. An environment-coupled molecularsystem that is comprised of a single level donor and acceptor species,‘dressed’ by a collective of bath vibrational modes, is used to modelthe charge transfer process. This leads to an equivalent circuit modelin which the dynamical variables describe wavefunction probabilityamplitudes. The impact of feedback on wavefunction probabilityamplitudes can then be described in terms of the dynamical variables ofthe circuit model.

“Meso”-scale properties in devices are usually observed at ultra-lowtemperatures and in high vacuum type environments, and these uniqueproperties can enable novel applications in many industries includingtiming references, memory, communications and sensing. However, thesemeso-structures are relatively unsuitable for practical deploymentbecause these properties manifest only for an idealized set ofconditions, and there is tremendous overhead needed to realize theseidealized conditions. With the feedback topology described herein, theseproperties can be realized at room temperatures and in “dirty” systems,making these devices a practical reality. The proposed topology can beeasily scaled, thus minimizing the space and energy overhead forrealizing such systems.

The equations of motion for a one dimensional particle (system) coupledto a bath of damping vibrational modes are given by:

$\begin{matrix}{{\overset{.}{x}(t)} = {\frac{p(t)}{m}\mspace{14mu}{and}}} & (1.1) \\{{{\overset{.}{p}(t)} = {{- {V^{\prime}(x)}} - {\int_{0}^{t}{\frac{{\overset{\_}{\gamma}\left( {t - t^{\prime}} \right)}{p\left( t^{\prime} \right)}}{m}{dt}^{\prime}}} + {\overset{\_}{\xi}(t)}}},} & (1.2)\end{matrix}$

where γ is the damping kernel, and m, k_(B), T, and V(x) are the systemmass, Boltzmann constant, bath temperature and conservative potential,respectively. ξ(t) is a Gaussian function with zero mean and correlationgiven by

ξ(t)ξ(0)

=mk_(B)T Re γ(t) in the classical limit.

Thus, the amplitude of thermal disturbance acting on the system isrelated to the dissipative force exerted by the environment, subject tothe assumption that the thermal reservoir is large enough such that thebath vibrational modes continue to stay in equilibrium throughout theirinteraction with the system. These equations of motion are derived fromthe Hamiltonian description of the system and the environment, in whichthe environment is modeled as a collection of non-interacting harmonicoscillators (h.o.) and the interaction between the system and theenvironment is bilinear in the environment h.o coordinates and thesystem coordinate, as shown below:

$\begin{matrix}\begin{matrix}{H = {H_{sys} + H_{env} + H_{i}}} \\{{= {\frac{p^{2}}{2\; m} + {V(x)} + {\sum\limits_{\alpha}\frac{p_{\alpha}^{2}}{2m_{\alpha}}} + {\frac{m_{\alpha}\omega_{\alpha}^{2}}{2}\left( {q_{\alpha} + {\frac{c_{\alpha}}{m_{\alpha}\omega_{\alpha}^{2}}x}} \right)^{2}}}},}\end{matrix} & (2)\end{matrix}$

-   -   where in addition to the interaction term,

${x{\sum\limits_{\alpha}{c_{\alpha}q_{\alpha}}}},$there is a compensation term,

${\sum\limits_{\alpha}{\left( {c_{\alpha}x} \right)^{2}/\left( {2m_{\alpha}\omega_{\alpha}^{2}} \right)}},$that accounts for the shift in bath coordinates as a result of couplingwith the system. In this framework, the damping kernel and thermalfluctuations are given by:

$\begin{matrix}{{\overset{\_}{\gamma}(t)} = {\frac{1}{m}{\sum\limits_{\alpha}{\frac{c_{\alpha}^{2}}{m_{\alpha}\omega_{\alpha}^{2}}e^{{- j}\;\omega_{\alpha}t}}}}} & (3.1) \\{{\overset{\_}{\xi}(t)} = {- {\sum\limits_{\alpha}{{c_{\alpha}\left( {q_{\alpha_{o}} + {j\frac{p_{\alpha_{o}}}{m_{\alpha}\omega_{\alpha}}}} \right)}e^{{- j}\;\omega_{\alpha}t}}}}} & (3.2)\end{matrix}$

-   -   with q_(α) _(o) and p_(α) _(o) being the randomly selected        initial values of the position and momentum coordinates of        vibrational mode α. Under the assumption that these values are        sampled from an equilibrium Boltzmann distribution, the        fluctuation dissipation relationship can be shown to hold        ξ(t)ξ(0)        =mk_(B)T Reγ(t), where Reγ(t) is the real part of the kernel.        The equivalent bath temperature as seen by the system is given        by        ξ(t)ξ(0)        /m Re γ(t). In the Markovian limit, when the environment-system        interaction is without memory, by γ(t)=2ηδ(t). The real part of        the parameter η would represent an effective viscosity in a        mechanical system, or could be interpreted as a linear        resistance in an oscillatory electrical circuit, such as the one        shown in FIG. 4B.

FIG. 4A illustrates a circuit model of an oscillator in contact with athermodynamic bath, with a classical excitation source applying a signalto the oscillator system via a dissipative contact, according to variousexample embodiments described herein. Before further describing thedrawings, it is noted that FIGS. 4A, 4B, 5, 6A, and 6B are provided toillustrate the concept of feedback and the attenuation of dissipationand noise according to the embodiments described herein. The applicationof this feedback to the elementary system illustrated in these figuresis also representative and provided to explain the concepts of theinvention, which includes feedback applied to various mesoscale (andpotentially other) charge transfer systems.

The system in question, whether quantum or classical, is stimulated bythe randomized environment-induced thermal disturbances, which arebalanced by the dissipative forces as it moves in the field described bythe potential. According to the embodiments, an electronicfeedback-based mechanism is proposed for the bandwidth-limited controlof these thermal disturbances and the related damping forces. The caseof electrical oscillators is considered here for demonstration purposes,but the proposed mechanism can be extended to mechanical systems aswell.

As described herein, a scheme is presented whereby the system isdecoupled from the physical reservoir with which it is in contact andcoupled to another bath of pre-specified spectral density, ensuringcontrol over the bath's effective ‘temperature’ and the dampingexperienced by the system. In that context, FIG. 4B illustrates a threeterminal working electrode (W.E.), reference electrode (R.E.), andcounter electrode (C.E.) feedback system for the application of the samesignal as shown in FIG. 4A to the oscillatory system, where gain in thefeedback loop attenuates the dissipative coupling to the environment.The feedback system shown in FIG. 4B can be relied upon to providefeedback to the three-electrode analog measurement topology circuit 1300shown in FIG. 13 of U.S. Patent Publication No. 2014/0043049, forexample, which also illustrates W.E., R.E., and C.E. electrodes. Theentire contents of U.S. Patent Publication No. 2014/0043049 are herebyincorporated herein in their entirety.

As shown in the example of FIG. 4B, a sequence of cascaded amplifiers A1and A2 is configured to deliver a high gain, corrective signalproportional to the difference between V_(set) and V_(ref) uponmeasurement of the reference voltage V_(ref). The measurement isperformed with a buffer amplifier A1 that has a high impedance input tominimize leakage currents in the measurement. The physical referenceelectrode (R.E.) for probing the reservoir voltage, V_(ref), is deemedideally to have zero source impedance, as is the physical counterelectrode (C.E.) that applies the corrective signal V_(x′) to thesystem. The circuit schematics in FIGS. 4A and 4B measure the currentsI_(x) and I_(x′), respectively, flowing through the system acrossdissipative elements X_(r) and X_(m), respectively, in response to theclassical voltage excitation bias applied at the reference electrode.

The respective transimpedance responses for the systems in FIGS. 4A and4B are:

$\begin{matrix}{I_{x} = {\frac{V_{set}}{X_{r} - {jY}_{s}}\mspace{14mu}{and}}} & (4.1`) \\{{I_{x^{\prime}} = \frac{A_{1}A_{2}V_{set}}{X_{m} - {jY}_{s} + {{A_{2}\left( {1 + A_{1}} \right)} \cdot \left( {- {jY}_{s}} \right)}}},} & (4.2)\end{matrix}$

-   -   where Y_(s) is the resonant component of the system, given by        Y_(s)=(1/ωC₁−ωL₁). A₁,A₂ are the gain functions of the        respective amplifiers; the dissipative elements, X_(r) and X_(m)        in (4.1, 4.2), have real and imaginary components obtained by        averaging over the ensemble of vibrational modes:

$\begin{matrix}{{X_{r}(\omega)} = {{{- j} \cdot \left\lbrack {{PP}{\int{d\;\Omega\;{g(\Omega)}\frac{c^{2}(\Omega)}{m\;\Omega^{2}}\frac{1}{\omega^{2} - \Omega^{2}}}}} \right\rbrack} + {2\;\pi\frac{{g(\omega)}{c^{2}(\omega)}}{m\;\omega^{2}}}}} & (4.3)\end{matrix}$

-   -   where the first term, which includes the principle part (symbol        PP) of the integral over the complex plane, is representative of        a resonant frequency shift and the real term is the dissipation        experienced by the oscillating system.

Thus, the response of the oscillatory system to thermal excitations isdictated by the ensemble-averaged lumped circuit representation of theenvironment-induced dissipation as well as by the ensemble-averaged‘dressing’ down of the resonant frequency of the system, also by theenvironment vibrational modes. In that context, FIG. 5 illustrates asimulation graph of the oscillation amplitude measured at C1 in FIG. 4B,for example, in response to a small signal AC excitation of about 0.4V,with and without feedback. For the LTSpice IV simulation, amplifierswere selected from its component library, and the following componentvalues were set: L1=0.198H, C1=142 nF, X_(r)=9878 ohm, and X_(s)=100kohm. Select values of the components were chosen as a representativeexample of how feedback attenuates the dissipative interaction betweenthe oscillatory system and its thermal environment.

As shown in FIG. 5, the application of high gain negative feedbackcancels the dissipation and the dressing down of the resonance asobserved. The thermal disturbances induced by the reservoir on thesystem are measured at the R. E. node. These disturbances can beestimated and referred to the input source V_(excitation) for theschematics in FIGS. 4A and 4B, as is standard practice in noise analysisin electronic circuits.

$\begin{matrix}{\left\langle V_{x}^{2} \right\rangle = {\frac{{Y_{s}}^{2}}{{{X_{r} - {jY}_{s}}}^{2}}\left\langle V_{X_{r}}^{2} \right\rangle}} & (5.1) \\{\left\langle V_{x^{\prime}}^{2} \right\rangle = {\frac{{{A_{1}A_{2}}}^{2}{Y_{s}}^{2}}{{{X_{m} - {jY}_{s} + {{A_{2}\left( {1 + A_{1}} \right)}\left( {- {jY}_{s}} \right)}}}^{2}}\left\langle V_{ref}^{2} \right\rangle}} & (5.2)\end{matrix}$

The input-referred noise at the reference node is obtained bysuperposing each voltage noise source in the feedback loop and referringthem to the input:

$\begin{matrix}{\left\langle V_{ref}^{2} \right\rangle = {{\left( {\frac{\left\langle V_{A_{1}}^{2} \right\rangle}{\Delta\; f_{A_{1}}} + \frac{\left\langle V_{B_{1}}^{2} \right\rangle}{\Delta\; f_{B_{1}}}} \right)\Delta\; f_{ref}{\frac{A_{1}A_{2}}{1 + {A_{1}A_{2}}}}^{2}} + {\left( {\frac{\left\langle V_{A_{2}}^{2} \right\rangle}{\Delta\; f_{A_{2}}} + \frac{\left\langle V_{X_{r}}^{2} \right\rangle}{\Delta\; f_{X_{r}}} + \frac{\left\langle V_{X_{m}}^{2} \right\rangle}{\Delta\; f_{X_{m}}}} \right)\Delta\; f_{ref}\frac{1}{{{1 + {A_{1}A_{2}}}}^{2}}}}} & (5.3)\end{matrix}$

-   -   and Δf_(i) is the bandwidth of the i-th voltage noise source.        For large X_(m) and A₁, small reference node bandwidth Δf^(ref)        and a sufficiently quiet feedback network, the system would        experience significantly smaller thermal disturbances, or a        lower equivalent bath temperature, than in the case without        feedback. The equivalent mode temperature for the oscillatory        system, when in equilibrium with the reservoir modes, is        estimated from the equipartition theorem as        T_(s)=(½πC_(s)k_(B))·∫        q_(s) ²        dω, where

$\begin{matrix}{{\left\langle q_{s}^{2} \right\rangle = {\frac{1/L_{s}^{2}}{\frac{X_{m}^{2}\omega^{2}}{L_{s}^{2}{{A_{1}A_{2}}}^{2}} + \left( {\omega_{s}^{2} - \omega^{2}} \right)^{2}}\frac{\left\langle V_{ref}^{2} \right\rangle}{\Delta\; f_{ref}}}},} & (5.4)\end{matrix}$

-   -   assuming |A₁A₂|>>1 and is independent of frequency, and for        which ω_(s) ²=1/L_(s)C_(s). Integrating over the frequency        domain yields:

$\begin{matrix}{{{{\left. T_{s} \right.\sim T} \cdot \left( {1 + \frac{X_{r}}{X_{m}}} \right)}\frac{{A_{1}A_{2}}}{{{1 + {A_{1}A_{2}}}}^{2}}} + {\left( \frac{\left\langle V_{A_{2}}^{2} \right\rangle}{\Delta\; f_{A_{2}}X_{m}k_{B}} \right)\frac{{A_{1}A_{2}}}{{{1 + {A_{1}A_{2}}}}^{2}}} + {\left( {\frac{\left\langle V_{A_{1}}^{2} \right\rangle}{\Delta\; f_{A_{1}}} + \frac{\left\langle V_{B_{1}}^{2} \right\rangle}{\Delta\; f_{B_{1}}}} \right)\frac{{A_{1}A_{2}}}{X_{m}k_{B}}{{\frac{A_{1}A_{2}}{1 + {A_{1}A_{2}}}}^{2}.}}} & (5.5)\end{matrix}$

In effect, the physical environment around the system is exchanged withthe bath of modes associated with the measurement and feedbackinstrumentation, which can be tailored for a lower equivalent bathtemperature by choosing components with minimal thermal noisecharacteristics. This method of electronic ‘cooling’ can be contrastedwith other active feedback-based methodologies in opto-mechanicalsystems that utilize a large gain to increase the dissipative couplingbetween the mechanical system and its single mode optical environment,pre-prepared in a low temperature state, for improved coolingefficiency.

Simulations of voltage noise spectral density for the oscillator nodesV_(x) in FIG. 4B and V_(x′) in FIG. 4B,

V_(x) ²

/Δf and

V_(x′) ²

/Δf, as functions of X_(r) are depicted in FIGS. 6A and 6B,respectively. The series LC construct representing the oscillator systemcreates a high Q bandpass filter as a result of dissipation attenuationby the feedback. As the simulations indicate, feedback ‘cools’ thesystem, with the largest damping kernel being cooled the most. Further,FIG. 6C illustrates a simulation of voltage noise spectral density forthe oscillator node V_(x′) in FIG. 6B with feedback as a function ofX_(m). A larger X_(m) results in a lower total voltage noise power,yielding a lower effective bath temperature. Also evident in FIG. 6C isthe reduction in total integrated noise power, and the equivalent systemmode temperature, with increasing X_(m).

The effect of feedback on mesoscale charge transfer systems is nowdescribed in detail, by referencing the simpler example developed aboveof a single oscillator in contact with a thermal environment. Thequantum dynamics of Hermitian Hamiltonians are known to correspond tothe coupled motion of classical mechanical or electrical oscillators.Specifically, the classical probability amplitudes describing thetime-dependent state of an oscillatory system are equivalent to thequantum amplitudes that characterize the evolution of the wavefunctionof an excited quantum system by a time-dependent Schrodinger's waveequation. Consider single energy level donor and acceptor states,immersed in a reservoir bath, and coupled to one another so as to excitean electronic transition from the electronic source to the sink, asfollows:

$\begin{matrix}\begin{matrix}{H = {H_{d} + H_{a} + H_{env} + H_{d - a} + H_{d - {env}} + H_{a - {env}}}} \\{= {\frac{{\overset{\_}{p}}_{1}^{2}}{2\; M_{1}} + \frac{M_{1}\omega_{1}^{2}{\overset{\_}{Q}}_{1}^{2}}{2} + \frac{{\overset{\_}{p}}_{2}^{2}}{2M_{2}} + \frac{M_{2}\omega_{2}^{2}{\overset{\_}{Q}}_{2}^{2}}{2} +}} \\{{\sum\limits_{\alpha}\frac{{\overset{\_}{p}}_{\alpha}^{2}}{2m_{\alpha}}} + \frac{m_{\alpha}\omega_{\alpha}^{2}{\overset{\_}{q}}_{\alpha}^{2}}{2} + {V_{12}{\overset{\_}{Q}}_{1}{\overset{\_}{Q}}_{2}} +} \\{\sum\limits_{\alpha}{\left( {{V_{1\;\alpha}{\overset{\_}{Q}}_{1}} + {V_{2\;\alpha}{\overset{\_}{Q}}_{2}}} \right){\overset{\_}{q}}_{\alpha}}}\end{matrix} & (6.1)\end{matrix}$

The ‘momentum’ and ‘position’ coordinates for the system and environmentcan be suitably non-dimensionalized as follows:

$\begin{matrix}{{{Q_{j} = {\left( \frac{M_{j}\omega_{j}}{\hslash} \right)^{1/2}{\overset{\_}{Q}}_{j}}};{p_{j} = {{\left( \frac{1}{M_{j}\omega_{j}\hslash} \right)^{1/2}{\overset{\_}{p}}_{j}\mspace{14mu} j} = 1}}},2,} & (6.2) \\{{{q_{\alpha} = {\left( \frac{m_{\alpha}\omega_{\alpha}}{\hslash} \right)^{1/2}{\overset{\_}{q}}_{\alpha}}};{p_{\alpha} = {\left( \frac{1}{m_{\alpha}\omega_{\alpha}\hslash} \right)^{1/2}{\overset{\_}{p}}_{\alpha}}}},{and}} & (6.3) \\{{{v_{12} = \frac{V_{12}}{\left( {M_{1}M_{2}\omega_{1}\omega_{2}} \right)^{1/2}}};{v_{j\;\alpha} = {{\frac{V_{j\;\alpha}}{\left( {M_{j}m_{\alpha}\omega_{j}\omega_{\alpha}} \right)^{1/2}}\mspace{14mu} j} = 1}}},2.} & (6.4)\end{matrix}$

The dynamics of the system and environment can be re-derived from themodified non-dimensionalized Hamiltonian:

$\begin{matrix}{{{{{\overset{.}{Q}}_{1}(t)} = {\omega_{1}p_{1}}};{{{\overset{.}{p}}_{1}(t)} = {{{- \omega_{1}}Q_{1}} + {v_{12}Q_{2}} + {\sum\limits_{\alpha}{v_{1\;\alpha}q_{\alpha}}}}}},} & (6.5) \\{{{{{\overset{.}{Q}}_{2}(t)} = {\omega_{2}p_{2}}};{{{\overset{.}{p}}_{2}(t)} = {{{- \omega_{2}}Q_{2}} + {v_{12}Q_{1}} + {\sum\limits_{\alpha}{v_{2\;\alpha}q_{\alpha}}}}}},\mspace{14mu}{and}} & (6.6) \\{{{{\overset{.}{q}}_{\alpha}(t)} = {\omega_{\alpha}p_{\alpha}}};{{{\overset{.}{p}}_{\alpha}(t)} = {{{- \omega_{\alpha}}q_{\alpha}} + {v_{1\;\alpha}Q_{1}} + {v_{2\;\alpha}{Q_{2}.}}}}} & (6.7)\end{matrix}$

Based on the dynamical equations of motion 6.5-6.7, an equivalentcircuit description of the inter-coupled, single electronic energylevel, donor and acceptor charge transfer system is proposed as shown inFIG. 7A. Particularly, FIG. 7A illustrates a circuit model for atwo-state electron energy transfer (EET) system coupled to an externalbath of reservoir modes according to various example embodimentsdescribed herein. The individual energy levels are modeled as resonantelements that are coupled to the physical environment or, in the case offeedback, to the bath reservoir of instrumentation modes dissipativelyvia resistors at the reference node. The reference node in FIG. 7Adefines the location where an external bias is applied, or where, in thefeedback case, a reference probe is inserted to measure the ‘energy’ ofone of the levels that the feedback loop constrains to a desiredsetpoint. In this context, the reference is deemed a proxy measure forthe second energy level in experimental systems where direct access tothe state energy is unavailable. In addition, a capacitor between aresonant unit and the reference probe models the non-dissipativecoupling between the energy levels. The ‘ground’ for the proposedcircuit model in FIG. 7A defines the energy ground state relative towhich the energy of the resonant elements (ω₁, ω₂) and the sourceexcitation signal (eV/ℏ) are measured.

Recasting the equations of motion in terms of the probability amplitudefor donor/acceptor states, Z_(1,2)=Q_(1,2)+jp_(1,2), as well as for theenvironment modes, Z_(α)=q_(α)+jp_(α),

$\begin{matrix}{{{{\overset{.}{Z}}_{1} + {j\;\omega_{1}Z_{1}}} = {{{jv}_{12}Z_{2}} - {\sum\limits_{\alpha}{v_{1\;\alpha}^{2}{\int_{0}^{t}{{dt}^{\prime}{Z_{1}\left( t^{\prime} \right)}e^{{- j}\;{\omega_{\alpha}{({t - t^{\prime}})}}}}}}} - {\sum\limits_{\alpha}{v_{1\;\alpha}v_{2\;\alpha}{\int_{0}^{t}{d\;\tau\;{Z_{2}(\tau)}e^{{- j}\;{\omega_{\alpha}{({t - \tau})}}}}}}} + {j{\sum\limits_{\alpha}{v_{1\;\alpha}Z_{\alpha\; 0}e^{{- j}\;\omega_{\alpha}t}}}}}},} & (6.8) \\{\mspace{79mu}{and}} & \; \\{{{{\overset{.}{Z}}_{2} + {j\;\omega_{2}Z_{2}}} = {{{jv}_{12}Z_{1}} - {\sum\limits_{\alpha}{v_{2\;\alpha}^{2}{\int_{0}^{t}{{dt}^{\prime}{Z_{2}\left( t^{\prime} \right)}e^{{- j}\;{\omega_{\alpha}{({t - t^{\prime}})}}}}}}} - {\sum\limits_{\alpha}{v_{2\;\alpha}v_{1\;\alpha}{\int_{0}^{t}{d\;\tau\;{Z_{1}(\tau)}e^{{- j}\;{\omega_{\alpha}{({t - \tau})}}}}}}} + {j{\sum\limits_{\alpha}{v_{2\;\alpha}Z_{\alpha\; 0}e^{{- j}\;\omega_{\alpha}t}}}}}},} & (6.9)\end{matrix}$

-   -   after integrating out the environment mode dynamics. The state        occupation probabilities may be estimated from

$P_{i} = {\frac{{Z_{i}}^{2}}{\sum\limits_{i}{Z_{i}}^{2}}.}$Z_(α0) is the randomly chosen initial value for the occupationprobability of mode α. The form of the dynamical equations 6.8 and 6.9constitute Hermitian generalizations of the Hamiltonian in equation 6.1with linear position and momentum off-diagonal coupling, which is alsoreferred to as a system of p&q coupled oscillators. Equations 6.8, 6.9can be transformed by a redefinition of the variables Z_(1,2)e^(jω)^(1,2) ^(t)={tilde over (Z)}_(1,2) and the first integral term on theR.H.S of equation 6.8 can be simplified as:

$\begin{matrix}\begin{matrix}{{- {\sum\limits_{\alpha}{v_{1\;\alpha}^{2}{\int_{0}^{t}{{dt}^{\prime}{Z_{1}\left( t^{\prime} \right)}e^{{- j}\;{\omega_{\alpha}{({t - t^{\prime}})}}}}}}}} = {{- {{\overset{\sim}{Z}}_{1}(t)}}{\int_{0}^{\infty}{d\;\tau^{\prime}{\sum\limits_{\alpha}{v_{1\;\alpha}^{2}e^{{- {j{({\omega_{\alpha} - \omega_{1}})}}}\tau^{\prime}}}}}}}} \\{{= {- {{{\overset{\sim}{Z}}_{1}(t)}\left\lbrack {{j\;{\Delta\omega}_{11}} + {\frac{1}{2}\gamma_{11}}} \right\rbrack}}},}\end{matrix} & (6.10)\end{matrix}$

-   -   where

${\Delta\;\omega_{11}} = {{PP}{\int{d\;\omega\;{g(\omega)}\frac{v_{1}^{2}(\omega)}{\omega_{1} - \omega}}}}$and γ₁₁=2πν₁(ω₁)g(ω₁) constitute an effective resonance shift anddamping kernel respectively. The last terms on the R.H.S. of equations6.8 and 6.9 constitute the noise source terms that thermally excite thetransfer events. Similar simplifications can be introduced for the otherintegral terms, resulting in equations 6.8 and 6.9 being rewritten as:

$\begin{matrix}{{{\overset{.}{Z}}_{1} = {{{- \left( {{j\;\omega_{1}} + {j\;{\Delta\omega}_{11}} + {\frac{1}{2}\gamma_{11}}} \right)}Z_{1}} + {\left( {{jv}_{12} - {j\;{\Delta\omega}_{12}} - {\frac{1}{2}\gamma_{12}}} \right)Z_{2}} + {j{\sum\limits_{\alpha}{v_{1\;\alpha}Z_{\alpha\; 0}e^{{- j}\;\omega_{\alpha}t}}}}}},} & (6.11) \\{\mspace{79mu}{and}} & \; \\{{{\overset{.}{Z}}_{2} = {{{- \left( {{j\;\omega_{2}} + {j\;{\Delta\omega}_{22}} + {\frac{1}{2}\gamma_{22}}} \right)}Z_{2}} + {\left( {{jv}_{12} - {j\;{\Delta\omega}_{21}} - {\frac{1}{2}\gamma_{21}}} \right)Z_{1}} + {j{\sum\limits_{\alpha}{v_{2\;\alpha}Z_{\alpha\; 0}e^{{- j}\;\omega_{\alpha}t}}}}}},} & (6.12)\end{matrix}$

-   -   with the parameters

${\Delta\;\omega_{ij}} = {{PP}{\int{d\;\omega\;{g(\omega)}\frac{{v_{i}(\omega)}{v_{j}(\omega)}}{\omega_{j} - \omega}}}}$and γ_(ij)=2πν_(i)(ω_(j))ν_(j)(ω_(j))g(ω_(j)).

Specific cases for large and small inter-level coupling (ν₁₂) areconsidered as asymptotic limits of the proposed ‘classical’ chargetransfer model. The model is simplified by the assumption that bathmodes for the two charge transfer component systems are identical, i.e.ν_(1α)=ν_(2α)=ν_(α) for all α, without any loss in generality. For thecase when ν₁₂>>max

$\left( {{{\omega_{1} - \omega_{2}}},{{\int_{0}^{\infty}{d\;\tau{\sum\limits_{\alpha}{v_{\alpha}^{2}e^{{- j}\;\omega_{\alpha}\tau}}}}}}} \right),$the eigenvalues of the system 6.11 and 6.12 are:

$\begin{matrix}{\Omega_{1} = {\frac{\omega_{1} + \omega_{2}}{2} - v_{12} + \left( {{\Delta\omega}_{11} + {\Delta\omega}_{22}} \right) - {j\frac{\left( {\gamma_{11} + \gamma_{22}} \right)}{2}}}} & \left( {6.13a} \right) \\{and} & \; \\{\Omega_{2} = {\frac{\omega_{1} + \omega_{2}}{2} + {v_{12}.}}} & \left( {6.13b} \right)\end{matrix}$

In the limit that Δω_(ii),γ_(ii)→0 for i=1, 2, the results in equations6.13a and 6.13b indicate the creation of new energy surfaces engenderedby a split of magnitude 2ν₁₂ in the strongly coupled h.o. wells ofenergy ω₁ and ω₂. The occupation probabilities for these new energysurfaces, as functions of time, are given by:P(ω=Ω₁ ,t:Δω _(ii),γ_(ii)→0)=1 and  (6.13c)P(ω=Ω₂ ,t:Δω _(ii),γ_(ii)→0)=0,  (6.13d)

-   -   for the case when the initial condition requires that the system        in populated in state ω₁. These results are indicative of an        adiabatic transfer process, characterized by a confinement of        the electronic charge to an adiabatic energy surface through the        process of transfer from the donor to the acceptor. On the other        hand, when ν₁₂→0, the eigenvalues are given by:

$\begin{matrix}{\Omega_{1} = {\omega_{1} + {\Delta\omega}_{11} - {j\frac{\gamma_{11}}{2}}}} & \left( {6.14a} \right) \\{and} & \; \\{{\Omega_{2} = {\omega_{2} + {\Delta\omega}_{22} - {j\frac{\gamma_{22}}{2}}}},} & \left( {6.14b} \right)\end{matrix}$

-   -   which is indicative of a diabatic crossing of the weakly coupled        h.o. wells, also for the limit of zero dissipation. The        corresponding probability that the system makes a quantum jump        from energy surface ω₁ to surface ω₂ at the crossing of the        diabatic curves is given by:

$\begin{matrix}{{P\left( {{\omega = \Omega_{2}},{t\text{:}{\Delta\omega}_{ii}},\left. \gamma_{ii}\rightarrow 0 \right.} \right)} = {v_{12}^{2}\frac{{\sin^{2}\left( \frac{\left( {\omega_{1} - \omega_{2}} \right)}{2} \right)}t}{\left( \frac{\omega_{2} - \omega_{1}}{2} \right)^{2}}}} & \left( {6.14c} \right) \\{and} & \; \\{{P\left( {{\omega = \Omega_{1}},{t\text{:}{\Delta\omega}_{ii}},\left. \gamma_{ii}\rightarrow 0 \right.} \right)} = {1 - {P\left( {{\omega = \Omega_{2}},{t\text{:}{\Delta\omega}_{ii}},\left. \gamma_{ii}\rightarrow 0 \right.} \right)}}} & \left( {6.14d} \right)\end{matrix}$in the limit of vanishingly small ν₁₂ and by ignoring the effects of theenvironment on the transition process. The transition probability asderived from equation 6.14c obeys Fermi's golden rule. The results inequations 6.13 and 6.14 confirm the applicability of the classical modelin describing charge transfer in the asymptotic limits of adiabatic anddiabatic transfer. The inclusion of the effects of the reservoir bath inthe estimation of the eigenfrequencies and of the transition rate forthe diabatic case indicates that the excitation due to the couplingbetween donor and acceptor states can be dissipated through the manymechanisms for energy-exchange that exist between the charge transfersystem and the external reservoir. Specifically, the interference termin equation 6.14c is now modified as:

$\begin{matrix}{{{\left. {P\left( {{\omega = \Omega_{2}},t} \right)} \right.\sim\frac{v_{12}^{2}}{\left( {\omega_{2} + {\Delta\omega}_{22} - \omega_{1} - {\Delta\omega}_{11}} \right)^{2} + \frac{\gamma_{11}^{2} + \gamma_{22}^{2}}{4}}}\left( {e^{{- \gamma_{11}}t} + e^{{- \gamma_{22}}t} + {2e^{{{- \gamma_{11}}{t/2}} - {\gamma_{22}{t/2}}}{\cos\left( {\omega_{2} + {\Delta\omega}_{22} - \omega_{1} - {\Delta\omega}_{11}} \right)}}} \right)} + {\frac{v_{12}^{2}}{\left( {\omega_{2} + {\Delta\omega}_{22} - \omega_{1} - {\Delta\omega}_{11}} \right)^{2} + \frac{\gamma_{11}^{2} + \gamma_{22}^{2}}{4}}{\quad\left\lbrack {{\sum\limits_{\alpha}{v_{\alpha}^{2}{Z_{\alpha\; 0}}^{2}\left. \quad\left( \begin{matrix}{\frac{e^{{- \gamma_{11}}t}}{\left( {\omega_{\alpha} - \omega_{1} - {\Delta\omega}_{11}} \right)^{2} + \frac{\gamma_{11}^{2}}{4}} +} \\{\frac{e^{{- \gamma_{22}}t}}{\left( {\omega_{2} + {\Delta\omega}_{22} - \omega_{\alpha}} \right)^{2} + \frac{\gamma_{22}^{2}}{4}} -} \\{\frac{e^{{{- {j{({\omega_{1} + {\Delta\omega}_{11}})}}}t} - {\gamma_{11}{t/2}} + {{j{({\omega_{2} + {\Delta\omega}_{22}})}}t} + {\gamma_{22}{t/2}}}}{\begin{matrix}\left( {{j\left( {\omega_{\alpha} - \omega_{1} - {\Delta\omega}_{11}} \right)} - {\gamma_{11}/2}} \right) \\\left( {j\left( {\omega_{2} - \omega_{\alpha}} \right)} \right)\end{matrix}} -} \\\frac{e^{{{+ {j{({\omega_{1} + {\Delta\omega}_{11}})}}}t} + {\gamma_{11}{t/2}} - {{j{({\omega_{2} + {\Delta\omega}_{22}})}}t} - {\gamma_{22}{t/2}}}}{\begin{matrix}\left( {{j\left( {{- \omega_{\alpha}} + \omega_{1} + {\Delta\omega}_{11}} \right)} + {\gamma_{11}/2}} \right) \\\left( {j\left( {\omega_{\alpha} - \omega_{2}} \right)} \right)\end{matrix}}\end{matrix} \right) \right\rbrack}} + {\sum\limits_{\alpha}{\frac{v_{\alpha}^{2}{Z_{\alpha\; 0}}^{2}}{\left( {\omega_{\alpha} - \omega_{2} - {\Delta\omega}_{22}} \right)^{2} + \frac{\gamma_{22}^{2}}{4}}\left\lbrack {1\left. \quad{{+ e^{{- \gamma_{22}}t}} - {2e^{{- \gamma_{22}}{t/2}}{\cos\left( {\omega_{2} + {\Delta\omega}_{22} - \omega_{\alpha}} \right)}t}} \right\rbrack} \right.}}} \right.}}} & \left( {6.14e} \right)\end{matrix}$

In addition to the damped interference between states seen as the firstterm on the R.H.S., the transition probability for the electron to makethe jump from energy surface Ω₁ to Ω₂ is also determined by indirectpaths through the environment by the inelastic exchange of energybetween the individual states Ω₁, Ω₂ and the reservoir modes that aredetermined by the density of states of the environmental modes and theircoupling strength to the charge transfer system, as seen in the secondterm on R.H.S. The third term denotes the scattering into and out of thestate Ω₂ due to the environment, independent of the transfer process.

The application of an electronic feedback mechanism to attenuate thedamping induced by the physical reservoir could, (a) reduce thenon-dissipative coupling between the two energy states, rendering theEET process diabatic, and/or (b) enable the preservation of the coherentinterference phenomena between vibronic states of the two-level systems.A simultaneous reduction in the r.m.s voltage fluctuations between theparticipant energy states by a low voltage-noise feedback mechanismwould also help suppress the background due to the inelastic processes.

In the context of an electronic feedback mechanism, FIG. 7B illustratesa feedback system coupled to the two-state EET system shown in FIG. 7Afor the attenuation of environment-induced dissipation according tovarious example embodiments described herein. FIGS. 7A and 7B are alsoprovided as representative illustrations of the use of feedback for theattenuation of dissipation and noise according to the embodimentsdescribed herein. Among the embodiments, this type of feedback can beapplied to various mesoscale charge transfer systems.

Here, the reference electrode or probe (R.E.) measures the energy of thequantum state 2, and the feedback sets the energy to a desired setpointvia a corrective signal applied to the energy of state 1. All stateenergies are measured relative to the system ground as mentionedpreviously. An ideal, dissipation-free reference probe is assumed incontact with the participant energy state 2 for the subsequent analysiswith Δω₂₂,γ₂₂→0. The analysis may be extended to the more general casewith dissipation in the reference channel. With the application offeedback, the probability amplitudes for the states of the twoparticipatory species in the charge transfer process are given by:

$\begin{matrix}{{Z_{1}\left( {V,\omega} \right)} = \frac{\begin{matrix}\left( {{{- {jv}_{12}}\frac{{j\;{\Delta\omega}_{11}} + {\gamma_{11}/2}}{\left( {{jv}_{12} + {j\;{\Delta\omega}_{11}} + {\gamma_{11}/2}} \right)}} + {j\left( {\frac{eV}{\hslash} - \omega_{2}} \right)}} \right) \\{\sum\limits_{\alpha}{v_{\alpha}Z_{\alpha\; 0}{\delta\left( {\frac{eV}{\hslash} - \omega_{\alpha}} \right)}}}\end{matrix}}{\begin{matrix}\left( {{j\;{\Delta\omega}_{11}} + {\gamma_{11}/2} + {j\left( {\frac{eV}{\hslash} - \omega_{1}} \right)}} \right) \\\left( {{{- {jv}_{12}}\frac{\left( {{j\;{\Delta\omega}_{11}} + {\gamma_{11}/2}} \right)}{\left( {{jv}_{12} + {j\;{\Delta\omega}_{11}} + {\gamma_{11}/2}} \right)}} + {j\left( {\frac{eV}{\hslash} - \omega_{2}} \right)}} \right) \\{\frac{1}{A_{1}{A_{2}(\omega)}} + {{j\left( {\frac{eV}{\hslash} - \omega_{1}} \right)} \cdot {j\left( {\frac{eV}{\hslash} - \omega_{2}} \right)}}}\end{matrix}}} & \left( {7.1a} \right) \\{and} & \; \\{{Z_{2}\left( {V,\omega} \right)} = \frac{{j\left( {\frac{eV}{\hslash} - \omega_{1}} \right)}{\sum\limits_{\alpha}{v_{\alpha}Z_{\alpha\; 0}{\delta\left( {\frac{eV}{\hslash} - \omega_{\alpha}} \right)}}}}{\begin{matrix}\left( {{j\;{\Delta\omega}_{11}} + {\gamma_{11}/2} + {j\left( {\frac{eV}{\hslash} - \omega_{1}} \right)}} \right) \\\left( {{{- {jv}_{12}}\frac{\left( {{j\;{\Delta\omega}_{11}} + {\gamma_{11}/2}} \right)}{\left( {{jv}_{12} + {j\;{\Delta\omega}_{11}} + {\gamma_{11}/2}} \right)}} + {j\left( {\frac{eV}{\hslash} - \omega_{2}} \right)}} \right) \\{\frac{1}{A_{1}{A_{2}(\omega)}} + {{j\left( {\frac{eV}{\hslash} - \omega_{1}} \right)} \cdot {j\left( {\frac{eV}{\hslash} - \omega_{2}} \right)}}}\end{matrix}}} & \left( {7.1b} \right)\end{matrix}$

In these descriptors for the probability amplitudes, the excitationsignal applied to the EET system via the feedback loop input, as shownin FIG. 7B, comprises two separable frequency components: a highfrequency part that characterizes the energy difference between the twoparticipant states (V) of the quantum mechanical charge transfer systemand a low frequency signal that describes the time response of theelectrical feedback mechanism (ω). In the asymptotic limit of largegain, the dynamic equations, as derived from Equations 7.1a and 7.1b,governing the evolution of the probability amplitudes are given by:

$\begin{matrix}{{{\overset{.}{Z}}_{1} = {{{- j}\;\omega_{1}Z_{1}} - {{j\left( {\omega_{2} - \omega_{1}} \right)}\frac{{jv}_{12}\left( {{j\;{\Delta\omega}_{11}} + {\gamma_{11}/2}} \right)}{{jv}_{12} + {j\;{\Delta\omega}_{11}} + {\gamma_{11}/2}}Z_{2}}}};} & \left( {7.2a} \right) \\{{Z_{1}(0)} = {{v\left( \omega_{1} \right)}{g\left( \omega_{1} \right)}Z_{10}}} & \; \\{and} & \; \\{{{{\overset{.}{Z}}_{2} = {{- j}\;\omega_{2}Z_{2}}};{{Z_{2}(0)} = {{v\left( \omega_{2} \right)}{g\left( \omega_{2} \right)}Z_{20}}}},} & \left( {7.2b} \right)\end{matrix}$

-   -   where the significantly slower dynamics of timescales ˜ω are        considered static as the probability amplitudes rapidly evolve        towards steady state. The eigenfrequencies for the charge        transfer system, in the limit of large gain, and for the        specific case of the dissipation-less reference probe are given        by:        Ω₁(Δω₂₂,γ₂₂→0)=ω1 and  (7.3a)        Ω₂(Δω₂₂,γ₂₂→0)=ω₂,  (7.3b)        which are independent of the non-dissipative coupling ν₁₂        between the participant species. The feedback decouples the        interacting energy states from one another and constrains the        EET process to be diabatic in nature. Therefore, a linear sweep        of the voltage at the reference node, where ω₂=ω₂ ^(o)−eV/ℏ, is        analogous to a scan of the energy of state 2. The r.m.s. voltage        noise determines the spread around the frequency ω₂, and a        low-noise voltage excitation signal mitigates this spread, which        is analogous to the effect of a cryostatic reduction in bath        temperature.

The participating species in the transfer process are indistinguishablefrom the environment at t=0 and the probability amplitudes ofenvironment modes of frequencies ω₁ and ω₂ are Z₁₀ and Z₂₀,respectively. The environment modes are assumed to evolve along adeterministic trajectory determined by the dynamics of the classicalexcitation signal, V, acting on the modes. As such, the amplitudes ofenvironment modes at energies ω₁ and ω₂ are described by theirrespective coherent state amplitudes as:

$\begin{matrix}{{Z_{10}(\omega)} = {\frac{1}{\left( {e\;\Delta\;{V/\hslash}} \right)^{1/2}\pi^{1/4}}{\exp\left( {- \frac{\left( {\omega - \omega_{1}} \right)^{2}}{2\left( {e\;\Delta\;{V/\hslash}} \right)^{2}}} \right)}}} & \left( {7.4a} \right) \\{and} & \; \\{{Z_{20}(\omega)} = {\frac{1}{\left( {e\;\Delta\;{V/\hslash}} \right)^{1/2}\pi^{1/4}}{{\exp\left( {- \frac{\left( {\omega - \omega_{2}} \right)^{2}}{2\left( {e\;\Delta\;{V/\hslash}} \right)^{2}}} \right)}.}}} & \left( {7.4b} \right)\end{matrix}$

Here, ΔV is the thermal r.m.s. voltage fluctuation of the excitationsignal, which is proportional to √{square root over (T)}. Thecorresponding initial conditions in Equations 7.2a and 7.2b would bemodified as:

$\begin{matrix}{{Z_{1}(0)} = {\int_{- \infty}^{\infty}{{v(\omega)}{g(\omega)}{Z_{10}(\omega)}}}} & \left( {7.5a} \right) \\{and} & \; \\{{Z_{2}(0)} = {\int_{- \infty}^{\infty}{{v(\omega)}{g(\omega)}{{Z_{20}(\omega)}.}}}} & \left( {7.5b} \right)\end{matrix}$

The spread about the environment mode frequencies ω₁ and ω₂, eΔV/ℏ,determines whether bath modes in the vicinity of the characteristicfrequencies are able to contribute to the evolution of the wavefunctionsfor the sub-systems 1 and 2 that are participating in the EET process.Minimization of the r.m.s voltage noise at the reference node of thefeedback loop or an equivalent reduction in bath temperature reduces thecontribution from these background processes for states 1 and 2. Thus,environment-induced scattering into and out of the electronic states 1and 2 are confined to bath modes that are resonant with the stateenergies ω₁ and ω₂.

The solution of the dynamical equations 7.2a and 7.2b yield the timeevolution of probability amplitudes for states 1 and 2:

$\begin{matrix}{{Z_{1}(t)} = {{{v\left( \omega_{1} \right)}{g\left( \omega_{1} \right)}{Z_{10}\left( {1 - \frac{{jv}_{12}\left( {{j\;{\Delta\omega}_{11}} + {\gamma_{11}/2}} \right)}{\left( {{jv}_{12} + {j\;{\Delta\omega}_{11}} + {\gamma_{11}/2}} \right)}} \right)}e^{{- j}\;\omega_{1}t}} + {{v\left( \omega_{2} \right)}{g\left( \omega_{2} \right)}{Z_{20}\left( \frac{{jv}_{12}\left( {{j\;{\Delta\omega}_{11}} + {\gamma_{11}/2}} \right)}{\left( {{jv}_{12} + {j\;{\Delta\omega}_{11}} + {\gamma_{11}/2}} \right)} \right)}e^{{- j}\;\omega_{2}t}\mspace{14mu}{and}}}} & \left( {7.6a} \right) \\{\mspace{79mu}{{{Z_{2}(t)} = {{v\left( \omega_{2} \right)}{g\left( \omega_{2} \right)}Z_{20}e^{{- j}\;\omega_{2}t}}},}} & \left( {7.6b} \right)\end{matrix}$for the ideal initial conditions of zero spread about the environmentmodes ω₁ and ω₂. The line width around the electronic state ω₁ is alsominimized by the attenuation of the dissipative coupling between state 1and its environment modes which has been described previously.Therefore, the primary EET process is constrained to an exchange ofenergy between the electronic energy level of state 1 and the bath modeat frequency ω₂, where each participant state energy level ischaracterized by a narrow spread.

The participant electronic states also exchange energy with bath modesthat are resonant with the respective electronic energies. State 1, forwhich the feedback attenuates the dissipative coupling with theenvironment modes, is also characterized by persistent spectralcoherence with the bath mode resonant with state 2 as seen in Equation7.6a. The interference between the electronic and vibronic states,observed within the dynamic variables Q₁, p₁ that characterize an EETparticipant, enables measurement of the vibronic structure of thecomplementary participant that is subject to the energy scan. Thismeasurement methodology is particularly useful where direct measurementof the dynamic variables of the complimentary participant in the EETprocess is not possible, for example in a molecular electrochemicalcharge transfer system, where state 2 characterizes a redox-activemolecule dissolved in a liquid electrolyte medium.

In summary, a feedback mechanism is proposed that attenuates dissipationfrom a thermodynamic bath to preserve coherent interferences betweenparticipant states in an EET process. A classical circuit analogy isshown to characterize the effect of electronic feedback on the quantumEET system. In addition, the dissipation-free state can probe thevibronic characteristics of the complimentary participant state throughthe suppression of the r.m.s. voltage fluctuations between the twostates using negative feedback.

EXAMPLE

A potentiostatic apparatus with a feedback control system detectsStaphylococcal Enterotoxin B in an electrolyte containing redox couplepotassium hexacyanoferrate (ii)/(iii). The concentration of the analytein the electrolyte ranges from 1 μg/ml to 1 μg/ml. The potentiostaticapparatus includes a counter electrode, a reference electrode and aworking electrode that are in electrical contact with the electrolyte.The counter, reference and working electrodes are made of metals (e.g.,gold, platinum, platinum-iridium, silver, silver/silver-chloride). Thepotentiostatic apparatus detects the potential of the redox activespecies in the electrolyte at the reference electrode, and based on thedetected potential, provides a low-noise high gain feedback currentsignal to the electrolyte via the counter electrode. The charge in thecurrent signal is carried between the counter electrode and the workingelectrode by mono and di-hydrogen phosphate anions and potassiumcations. The working electrode is grounded (i.e., connected to a groundpotential), and the charge received by the working electrode istransferred to the ground.

The reference electrode is electrically coupled to a voltage buffer viaan impedance. The voltage buffer includes an nMOS transistor cascadedwith another nMOS transistor. The drain of the first nMOS transistor iselectrically connected to a voltage source with potential +V_(B), andthe gate of the first nMOS transistor is electrically coupled to thereference electrode via an impedance X_(ref). The drain of the secondnMOS transistor is electrically connected to the source of an nMOStransistor via impedance R_(B1). The source of the second nMOStransistor is electrically connected to a voltage source with potential−V_(B) via impedance R_(B2). Additionally, the gate of the nMOStransistor electrically connected to a voltage source with potential−V_(B). The potential at the drain of the second nMOS transistor is theoutput V_(meas) of the voltage buffer.

A pair of cascaded high gain amplifiers can deliver a high gaincorrective signal to the electrolyte via the counter electrode. Thefirst high gain amplifier receives a set potential V_(set) (at invertinginput terminal), and the output of the voltage buffer V_(meas) (at noninverting input terminal) as inputs. The output of the first gainamplifier is connected to the inverting input terminal of the first highgain amplifier by a resistor R_(F1). The output of the first high gainamplifier is electrically connected to the inverting input terminal ofthe second high gain amplifier via resistor R_(S2). The non-invertinginput terminal of the second amplifier is connected to a groundpotential. The output of the second high gain amplifier is connected tothe inverting input terminal of the second high gain amplifier by aresistor R_(F2). The output of the second high gain amplifier(corrective feedback current signal) is electrically connected to thecounter electrode via resistor X_(M).

The corrective feedback current signal is detected by measuring thevoltage across the resistor X_(M) using a low noise voltmeter or atransimpedance amplifier. The corrective feedback current signaldetermines the potential of the counter electrode and suppressesdissipation acting on the charge transfer process, as well as thethermal voltage fluctuations acting on the species in the electrolyte.The corrective feedback signal can, thus, affect the electronic exchangeprocess at the working electrode. The corrective feedback signal canchange when the set potential V_(set) is changed. The voltmeter detectsthe change in the corrective feedback current for different values ofthe set potential V_(set). The voltmeter is connected to a controller(e.g., general purpose computer) that changes the value for the setpotential V_(set) and records the corresponding corrective feedbackcurrent. As a result, the controller generates current versus voltagedata for the electrolyte with the analyte. An analytics routine thencompares the signatures in the acquired I-V trace with those in areference database to ascertain the identity of the analyte.

What is claimed is:
 1. A system comprising: (a) a plurality ofelectrodes configured to electrically couple to an electrochemicalsystem; and (b) a feedback mechanism coupled to a first electrode of theplurality of electrodes and configured to detect a potential associatedwith the electrochemical system via the first electrode, wherein thefeedback mechanism provides a feedback signal to the electrochemicalsystem via a second electrode of the plurality of electrodes, thefeedback signal configured to provide excitation control of theelectrochemical system at a third electrode of the plurality ofelectrodes, wherein the feedback mechanism comprises a firstnegative-feedback amplifier configured to generate a first signal basedon a difference between the detected potential and a set potentialvalue.
 2. The system of claim 1, wherein the feedback signal providesexcitation control of an electrolyte in the electrochemical systemduring electronic excitation transfer (EET) in the electrochemicalsystem.
 3. The system of claim 2, wherein the excitation controlattenuates thermal disturbances in electric field in proximity to thethird electrode due to electronic noise injected into theelectrochemical system from the first electrode and the secondelectrode.
 4. The system of claim 2, wherein the excitation controlreduces dissipation in the charge transfer between one or more vibronicenergy levels of redox species and the third electrode.
 5. The system ofclaim 1, wherein the first, second, and third electrodes are a referenceelectrode, a counter electrode, and a working electrode of apotentiostat, respectively.
 6. The system of claim 1, wherein thefeedback mechanism comprises a second negative feedback amplifierconfigured to receive the first signal and generate the feedback signal.7. The system of claim 1, comprising a current detection systemconfigured to detect a current associated with the second electrode. 8.The system of claim 7, wherein the current associated with the secondelectrode is indicative of an analyte in the electrochemical system. 9.The method of claim 1, wherein the feedback mechanism comprises a secondnegative feedback amplifier configured to receive the first signal andgenerate the feedback signal.
 10. A method of analyte detectioncomprising: (a) detecting, by a feedback mechanism via a first electrodeof a plurality of electrodes, a potential associated with anelectrochemical system, wherein the plurality of electrodes areelectrically coupled to the electrochemical system; (b) generating, bythe feedback mechanism, a feedback signal; and (c) providing thefeedback signal to the electrochemical system via a second electrode ofthe plurality of electrodes, the feedback signal configured to provideexcitation control of the electrochemical system at a third electrode ofthe plurality of electrodes wherein the feedback mechanism comprises afirst negative-feedback amplifier configured to generate a first signalbased on a difference between the detected potential and a set potentialvalue.
 11. The method of claim 10, wherein the feedback signal providesexcitation control of an electrolyte in the electrochemical duringelectronic excitation transfer (EET) in the electrochemical system. 12.The method of claim 11, wherein the excitation control attenuatesthermal disturbances in electric field in proximity to the thirdelectrode due to electronic noise injected into the electrochemicalsystem from the first electrode and the second electrode.
 13. The methodof claim 11, wherein the excitation control reduces dissipation in thecharge transfer between one or more vibronic energy levels of redoxspecies and the third electrode.
 14. The method of claim 10, wherein thefirst, second, and third electrodes are a reference electrode, a counterelectrode, and a working electrode of a potentiostat, respectively. 15.The method of claim 10, further comprising detecting, via a currentdetection system, a current associated with the second electrode. 16.The method of claim 15, wherein the current associated with the secondelectrode is indicative of an analyte in the electrochemical system.